This invention provides ethylene copolymer fine particles and functional group-containing ethylene copolymer fine particles, which satisfy the following requirements (A) to (E), have a smaller particle diameter than the conventional particulate polyethylene, do not cause aggregation among the fine particles, have a very narrow particle size distribution, and a high level of roundness. Nonaggregative spherical magnesium-containing fine particles are also provided which are usable as a magnesium-containing carrier component for an olefin polymerization catalyst capable of producing the above fine particles. (Requirements) (A) An intrinsic viscosity [] of 0.1 to 50 dl/g as measured in decalin at 135 C, (B) a passage rate, through a mesh sieve with an opening of 37 [mu]m, of not less than 95% by weight, (C) a median size (d50) of 3 [mu]m = d50 = 25 [mu]m as measured by a laser diffraction scattering method, (D) a circularity coefficient of not less than 0.85, and (E) a coefficient of variation(Cv) of not more than 20%.